Tagged Questions

In cryptography, a discrete logarithm is the number of times a generator of a group must be multiplied by itself to produce a known number. By choosing certain groups, the task of finding a discrete logarithm can be made intractable.

Let's suppose we are using the exponential ElGamal as a public-key encryption scheme, so that we encrypt $g^m$ instead of $m$, for some generator $g$. Let $x$ be the private key, and $h=g^x$ be the ...

El Gamal encryption involves picking $(p,g,b)$ which is our public key. We compute $b=a^x$ $mod$ $p$. Here, $x$ is the private key which we don't know.
What are some efficient and strong algorithms ...

I understand how ECC is based on the discrete log problem and RSA on integer factorization. I've read several references that show how a solution to either of these problems can typically be adapted ...

How are the three problems Discrete Logarithm, Computational Diffie-Hellman and Decisional Diffie-Hellman related?
From my understanding, since the Discrete Log (DL) Problem is considered hard, then ...

A recent paper by Göloğlu, Granger, McGuire, and Zumbrägel: Solving a 6120-bit DLP on a Desktop Computer seems to "demonstrate a practical DLP break in the finite field of $2^{6120}$ elements, using ...

The most common groups to be used as examples for the DH protocol are modular multiplication and elliptic curves. But I've realised that the groups doesn't need to be finite, a suitable infinite group ...

I take the definition of safe prime as: a prime $p$ is safe when $(p-1)/2$ is prime.
Safe primes of appropriate size are the standard choice for the modulus of cryptosystems related to the discrete ...

The wiki defines the decisional Diffie–Hellman assumption as follows:
Decisional Diffie–Hellman assumption
Consider a (multiplicative) cyclic group $G$ of order $q$, and with generator $g$. The DDH ...

This question is a companion to the equivalent question on elliptic curves.
Preliminaries
Diffie-Hellman, Elgamal, DSA, etc. are examples of protocols that work in the integers modulus a large prime ...

Sometimes the easiest way to describe security of a type of cryptography is to say that "the time it takes to solve for an x-bit key would be y years". How would one go about doing such a calculation ...

I was wondering whether it is safe to use the same DH or ECDH key pair in more than one key agreement, particularly if these public keys are in a public registry. These public keys could be used by ...

Suppose $g$ is a generator of an order $p$ cyclic group in which discrete logarithm is hard and $p$ is a prime (i.e., given $g^x$ for a random $x \in \{0,1,\ldots, p-1\}$, it is hard to recover $x$ ...